Finite Group Databasebeta

← #18077232

Subgroups — #18077232

Order 4864.

908 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572664C211yesmaximal, characteristic, complemented
2C4×#10597383C211yesmaximal, characteristic
3#14563544C212yesmaximal, complemented
4#14561481C212yesmaximal, complemented
5C19×#1459C211yesmaximal, characteristic, complemented
6C23×C4×D19C2211yescharacteristic
7C2×#10597383C411yescharacteristic
8C2×C4×C22⋊D19—21no—
9#11926616—24no—
10#11926601—21no—
11#11926508—21no—
12C2×C22⋊(C19⋊C8)C2212yes—
13C2×(C2×D19)⋊C8—24no—
14#11926424C411yescharacteristic
15#11926420—21no—
16#11926416C411yescharacteristic
17#11926415—21no—
18#11926399C411yescharacteristic
19C4×(C2×D19)⋊C4—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21C2×C4×D4×C19C2211yescharacteristic
22C2×C19×C22⋊C8C2212yes—
23C19×#324—21no—
24C19×#323—21no—
25C24×D19C2×C411yescharacteristic
26C22×D4×C19C2×C411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19—21no—
30C23×Dic19C2×C411yescharacteristic
31C22×C4×D19—21no—
32C22×C4×D19—22no—
33C22×C4×D19—21no—
34C22×C4×D19—22no—
35C22×C4×D19—44no—
36C22×C8×C19—22no—
37C4×D4×C19—22no—
38C4×D4×C19—22no—
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C22⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19C2×C411yescharacteristic
45C2×C22⋊Dic19C2×C411yescharacteristic
46#10597383—22no—
47#10597383—22no—
48C4×C22⋊D19—44no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—21no—
52C2×Dic19⋊C4—21no—
53C2×C4×Dic19—21no—
54C2×#64520—22no—
55C22×C19⋊C8D414yescomplemented
56C19×C22⋊C8—22no—
57C19×C22⋊C8—22no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61C22⋊(C19⋊C8)—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64(C2×D19)⋊C8—48no—
65C4⋊(C19⋊C8)—22no—
66#10597260—22no—
67C24×C19C22⋊C411yescharacteristic
68C24×C19C22×C411yescharacteristic
69C23×D19—21no—
70C23×D19—22no—
71C23×D19—21no—
72C23×D19—22no—
73C23×D19—42no—
74C23×D19—42no—
75C23×D19M1612yescomplemented
76C2×D4×C19—22no—
77C2×D4×C19—21no—
78C2×D4×C19—21no—
79C2×D4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19C22⋊C411yescharacteristic
85C22×C4×C19C22⋊C411yescharacteristic
86C22×C4×C19C22⋊C411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4112yes—
91C2×C22⋊D19—24no—
92C2×C22⋊D19—42no—
93C2×C22⋊D19—42no—
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—22no—
97C22×Dic19—21no—
98C22×Dic19—42no—
99C2×C4×D19—28no—
100C2×C4×D19—24no—
101C2×C4×D19—42no—
102C2×C4×D19—44no—
103C2×C4×D19—44no—
104C2×C4×D19—42no—
105C2×C4×D19—42no—
106C2×C4×D19—44no—
107C2×C4×D19—41no—
108C2×C4×D19—42no—
109C2×C4×D19—41no—
110C2×C8×C19—44no—
111C2×C8×C19—42no—
112C4⋊C4×C19—22no—
113C22⋊C4×C19—22no—
114C22⋊C4×C19—22no—
115C42×C19—21no—
116C42×C19—21no—
117C22⋊Dic19—21no—
118C22⋊Dic19—22no—
119C22⋊Dic19—42no—
120C22⋊Dic19M1612yescomplemented
121(C2×D19)⋊C4—24no—
122(C2×D19)⋊C4—42no—
123(C2×D19)⋊C4—42no—
124Dic19⋊C4—42no—
125C4×Dic19—42no—
126#64520—82no—
127C2×C19⋊C8—24no—
128C2×C19⋊C8—44no—
129#8967—191nomaximal, Sylow
130C23×C19—21no—
131C23×C19—21no—
132C23×C19—21no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19C2×C22⋊C411yescharacteristic
138C23×C19C4×D412yes—
139C23×C19C2×M1611yescharacteristic
140C23×C19C2×M1611yescharacteristic
141C23×C19#13112yes—
142C22×D19—22no—
143C22×D19—22no—
144C22×D19—24no—
145C22×D19—24no—
146C22×D19—22no—
147C22×D19—24no—
148C22×D19—44no—
149C22×D19—44no—
150C22×D19—48no—
151C22×D19—41no—
152C22×D19—42no—
153C22×D19—41no—
154C22×D19—42no—
155C22×D19—41no—
156C22×D19—41no—
157C22×D19—42no—
158D4×C19—42no—
159D4×C19—42no—
160C2×C4×C19—24no—
161C2×C4×C19—22no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—21no—
165C2×C4×C19—21no—
166C2×C4×C19—21no—
167C2×C4×C19—41no—
168C2×C4×C19—42no—
169C2×C4×C19—42no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—81no—
173C2×C4×C19#12011yescharacteristic
174C2×C4×C19#12112yes—
175C2×C4×C19#12311yescharacteristic
176C22⋊D19—48no—
177C2×Dic19—22no—
178C2×Dic19—24no—
179C2×Dic19—22no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—42no—
183C2×Dic19—41no—
184C2×Dic19—41no—
185C2×Dic19—41no—
186C2×Dic19—41no—
187C2×Dic19—41no—
188C4×D19—48no—
189C4×D19—44no—
190C4×D19—44no—
191C8×C19—82no—
192C19⋊C8—44no—
193#2973—191no—
194C4×#120—191no—
195#1779—192no—
196#1459D1911yescharacteristic, complemented
197#1282—192no—
198C22×C19—21no—
199C22×C19—22no—
200C22×C19—21no—
201C22×C19—22no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19—42no—
205C22×C19—42no—
206C22×C19—41no—
207C22×C19—41no—
208C22×C19—41no—
209C22×C19—81no—
210C22×C19#38611yescharacteristic
211C22×C19#40711yescharacteristic
212C22×C19#40811yescharacteristic
213C22×C19#43512yes—
214C22×C19#43612yes—
215C2×D19—24no—
216C2×D19—28no—
217C2×D19—42no—
218C2×D19—42no—
219C2×D19—42no—
220C2×D19—44no—
221C2×D19—44no—
222C2×D19—44no—
223C2×D19—42no—
224C2×D19—42no—
225C2×D19—42no—
226C4×C19—22no—
227C4×C19—21no—
228C4×C19—41no—
229C4×C19—41no—
230C4×C19—41no—
231C4×C19B(4,𝔽2)12yes—
232Dic19—42no—
233Dic19—42no—
234Dic19—81no—
235C24×C4—191no—
236C2×#120—191no—
237C2×C4×D4—381no—
238C2×C4×D4C2×D1911yescharacteristic
239#435—384no—
240#432—381no—
241#407—381no—
242C2×C22⋊C8—192no—
243C2×C22⋊C8—384no—
244C2×C22⋊C8C2×D1912yes—
245#386—191no—
246#386—381no—
247#385—191no—
248#385—381no—
249#379—191no—
250C4×C22⋊C4—191no—
251C4×C22⋊C4—381no—
252#324—21no—
253#323—21no—
254C2×C19—21no—
255C2×C19—21no—
256C2×C19—22no—
257C2×C19—22no—
258C2×C19—81no—
259C2×C19#187011yescharacteristic
260C2×C19#188911yescharacteristic
261C2×C19#189111yescharacteristic
262D19—44no—
263C25—191no—
264C22×D4—381no—
265C22×D4C4×D1911yescharacteristic
266C23×C4—191no—
267C23×C4—381no—
268C23×C4—382no—
269C23×C4—382no—
270C23×C4—381no—
271C23×C4—764no—
272C23×C4D7611yescharacteristic
273C23×C4C22×D1911yescharacteristic
274C2×M16—382no—
275C22×C8—22no—
276C22×C8—194no—
277#120—382no—
278#120—382no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—764no—
282C2×C4⋊C4—381no—
283C2×C4⋊C4C22⋊D1911yescharacteristic
284C2×C22⋊C4—191no—
285C2×C22⋊C4—191no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—381no—
289C2×C22⋊C4—381no—
290C2×C22⋊C4C4×D1911yescharacteristic
291C2×C22⋊C4C22⋊D1911yescharacteristic
292C2×C42—381no—
293C2×C42D7611yescharacteristic
294C4⋊C8—382no—
295C22⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8—382no—
298C22⋊C8—382no—
299C22⋊C8—382no—
300C22⋊C8—768no—
301#97—382no—
302#95—381no—
303#95—381no—
304#95—381no—
305C19#896711yescharacteristic, complemented, Sylow
306C24—192no—
307C24—382no—
308C24—381no—
309C24—382no—
310C24—381no—
311C24—762no—
312C24—762no—
313C24(C2×D19)⋊C411yescharacteristic
314C24C2×C4×D1911yescharacteristic
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—384no—
320C2×D4—762no—
321C2×D4—762no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—388no—
327C22×C4—384no—
328C22×C4—382no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4—762no—
333C22×C4—764no—
334C22×C4—764no—
335C22×C4—762no—
336C22×C4—764no—
337C22×C4—762no—
338C22×C4—762no—
339C22×C4—762no—
340C22×C4—761no—
341C22×C4—761no—
342C22×C4(C2×D19)⋊C411yescharacteristic
343C22×C4(C2×D19)⋊C411yescharacteristic
344C22×C4(C2×D19)⋊C411yescharacteristic
345C22×C4C2×D7611yescharacteristic
346C22×C4D4×D1912yes—
347C22×C4#6454312yes—
348C22×C4C2×C22⋊D1911yescharacteristic
349M16—1522no—
350C2×C8—44no—
351C2×C8—42no—
352C2×C8—384no—
353C2×C8—764no—
354C4⋊C4—22no—
355C4⋊C4—762no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—192no—
359C22⋊C4—384no—
360C22⋊C4—381no—
361C22⋊C4—382no—
362C22⋊C4—762no—
363C22⋊C4—762no—
364C22⋊C4—762no—
365C42—21no—
366C42—21no—
367C42—762no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—382no—
376C23—382no—
377C23—384no—
378C23—384no—
379C23—384no—
380C23—382no—
381C23—761no—
382C23—762no—
383C23—761no—
384C23—762no—
385C23—764no—
386C23—768no—
387C23—764no—
388C23—762no—
389C23—761no—
390C23—761no—
391C23(C22⋊D19)⋊C412yes—
392C23#1059734712yes—
393C23M16×D1911yescharacteristic
394C23M16×D1911yescharacteristic
395C23C2×(C2×D19)⋊C411yescharacteristic
396D4—42no—
397D4—42no—
398D4—768no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—382no—
413C2×C4—384no—
414C2×C4—382no—
415C2×C4—768no—
416C2×C4—764no—
417C2×C4—761no—
418C2×C4—761no—
419C2×C4—762no—
420C2×C4—761no—
421C2×C4—761no—
422C2×C4—764no—
423C2×C4—761no—
424C2×C4—761no—
425C2×C4—761no—
426C2×C4#1059732811yescharacteristic
427C2×C4#1059733211yescharacteristic
428C2×C4#1059738512yes—
429C8—82no—
430C8—764no—
431C22—21no—
432C22—22no—
433C22—21no—
434C22—22no—
435C22—42no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—81no—
443C22—384no—
444C22—388no—
445C22—762no—
446C22—762no—
447C22—762no—
448C22—764no—
449C22—764no—
450C22—764no—
451C22—762no—
452C22—762no—
453C22—762no—
454C22#1192642111yescharacteristic
455C22#1192650711yescharacteristic
456C22#1192651011yescharacteristic
457C22#1192661812yes—
458C22#1192661912yes—
459C4—22no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—762no—
465C4—762no—
466C4—1521no—
467C4#1192673212yes—
468C2—21no—
469C2—21no—
470C2—22no—
471C2—22no—
472C2—81no—
473C2—764no—
474C2#1456393011yescharacteristic
475C2#1456404111yescharacteristic
476C2#1456405111yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1459C2
socleC22×C19#386
prime radicalC2×#10597383C4
cosocleC23×C4×C19C23
hypercenter#1459D19
hypocenterC19#8967
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14572664C2semidirect
3. #14563544C2semidirect
4. #14561481C2semidirect
5. C19×#1459C2semidirect
55. C22×C19⋊C8D4semidirect
75. C23×D19M16semidirect
120. C22⋊Dic19M16semidirect
196. #1459D19semidirect
305. C19#8967semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145726642
C4×#105973832
#145635442
#145614812
C19×#14592
#896719